CEMC Euclid, 2000

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

On a cross-sectional diagram of the Earth, the $x$ and $y$ -axes are placed so that $O(0,0)$ is the centre of the Earth and $C(6.40, 0.00)$ is the location of Cape Canaveral. A space shuttle is forced to land on an island at $A(5.43, 3.39)$ , as shown. Each unit represents $1\,000$ km. Determine the distance from Cape Canaveral to the island, measured on the surface of the earth, to the nearest 10 km.

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